function y = kernel_m_singular_mod_analytical(zeta, m, CONSTS, n_beg_sum)

    k0 = CONSTS.k0;
    a = CONSTS.a;
    eps = CONSTS.eps;
    eta = CONSTS.eta;
    c = CONSTS.c;
    
    Z0 = 4*pi/c;
    
    y = 1i*Z0*(k0/(2*pi))*((-(4*m^2*1i)/((k0*a)^2*sqrt(eps*abs(eta))))*(log(abs(zeta)./(2*a)) + ...
        log(pi*sqrt(eps/abs(eta))) + 1i*pi/2 + 2*((sum(1./(2*(1:(abs(m)+2*n_beg_sum + 1))-1))) - log(2))));

end